Classification of Almost Quarter-pinched Manifolds
نویسنده
چکیده
We show that if a simply connected manifold is almost quarter pinched then it is di¤eomorphic to a CROSS or sphere.
منابع مشابه
Manifolds with Pointwise 1/4-pinched Curvature
In this lecture we will describe our recent joint work with SimonBrendle ([1], [2]) in which we give the differentiable classification ofcompact Riemannian manifolds with pointwise 1/4-pinched curvature.Our theorems are:Theorem 1. Let M be a compact Riemannian manifold with pointwise1/4-pinched curvature. Then M admits a metric of constant curvature,and therefore is ...
متن کاملClassification of Manifolds with Weakly 1/4-pinched Curvatures Simon Brendle and Richard Schoen
A classical theorem due to M. Berger [2] and W. Klingenberg [11] states that a simply connected Riemannian manifold whose sectional curvatures all lie in the interval [1, 4] is either isometric to a symmetric space or homeomorphic to Sn (see also [12], Theorems 2.8.7 and 2.8.10). In this paper, we provide a classification, up to diffeomorphism, of all Riemannian manifolds whose sectional curvat...
متن کاملAlmost Quarter-pinched Kähler Metrics and Chern Numbers
Given n ∈ Z and ε > 0, we prove that there exists δ = δ(ε, n) > 0 such that the following holds: If (M, g) is a compact Kähler n-manifold whose sectional curvatures K satisfy
متن کاملKähler manifolds and fundamental groups of negatively δ-pinched manifolds
In this note, we will show that the fundamental group of any negatively δ-pinched (δ > 14) manifold can’t be the fundamental group of a quasi-compact Kähler manifold. As a consequence of our proof, we also show that any nonuniform lattice in F4(−20) cannot be the fundamental group of a quasi-compact Kähler manifold. The corresponding result for uniform lattices was proved by Carlson and Hernánd...
متن کاملar X iv : m at h / 02 08 19 7 v 1 [ m at h . D G ] 2 6 A ug 2 00 2 Hyperbolic Rank of Products
Generalizing [BrFa] we prove the existence of a bilipschitz embedded manifold of pinched negative curvature and dimension m1 +m2 −1 in the product X := Xm1 1 ×X m2 2 of two Hadamard manifolds Xmi i of dimension mi with pinched negative curvature. Combining this result with [BuySch] we prove the additivity of the hyperbolic rank for products of manifolds with pinched negative curvature.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2008